Geometric Mechanics
1. Edition November 1999
XXVIII, 554 Pages, Softcover
Textbook
Short Description
Not just another book on mechanics, Geometric Mechanics sets itself apart in important ways. It offers a modern treatment of classical mechanics, including material on relativistic physics, chaos theory, and nonlinear dynamics in addition to standard topics. It also stresses geometry, thereby focusing on the physical lines of reasoning rather than mathematical formalism.
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Further versions
Mechanics for the nonmathematician-a modern approach
For physicists, mechanics is quite obviously geometric, yet the classical approach typically emphasizes abstract, mathematical formalism. Setting out to make mechanics both accessible and interesting for nonmathematicians, Richard Talman uses geometric methods to reveal qualitative aspects of the theory. He introduces concepts from differential geometry, differential forms, and tensor analysis, then applies them to areas of classical mechanics as well as other areas of physics, including optics, crystal diffraction, electromagnetism, relativity, and quantum mechanics. For easy reference, Dr. Talman treats separately Lagrangian, Hamiltonian, and Newtonian mechanics-exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. Practical perturbative methods of approximation are also developed. Geometric Mechanics features illustrative examples and assumes only basic knowledge of Lagrangian mechanics.
Of related interest . . .
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A contemporary look at dynamics at an intermediate level, including nonlinear and chaotic dynamics.
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MATHEMATICAL PHYSICS
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A comprehensive treatment of the mathematical methods used to solve practical problems in physics and engineering.
1998 (0-471-15431-8) 680 pp.
Review of Solvable Systems.
THE GEOMETRY OF MECHANICS.
Geometry of Mechanics I: Linear.
Geometry of Mechanics II: Curvilinear.
Geometry of Mechanics III: Multilinear.
LAGRANGIAN MECHANICS.
Lagrange-Poincaré Description of Mechanics.
Simplifying the Poincaré Equation With Group Theory.
Conservation Laws and Symmetry.
NEWTONIAN MECHANICS.
Gauge-Invariant Mechanics.
Geometric Phases.
HAMILTONIAN MECHANICS.
Hamiltonian Treatment of Geometric Optics.
Hamilton-Jacobi Theory.
Relativistic Mechanics.
Symplectic Mechanics.
APPROXIMATE METHODS.
Analytic Basic for Approximation.
Linear Systems.
Perturbation Theory.
Index.
